Problem: Simplify the following expression: $a = \dfrac{p}{9} + \dfrac{3p}{7}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $9$ and $7$ $\lcm(9, 7) = 63$ $ a = \dfrac{7}{7} \cdot \dfrac{p}{9} + \dfrac{9}{9} \cdot \dfrac{3p}{7} $ $a = \dfrac{7p}{63} + \dfrac{27p}{63}$ $a = \dfrac{7p +27p}{63}$ $a = \dfrac{34p}{63}$